Subspace Rhapsody

James Kirk, recently promoted to executive officer of the Farragut, visits the Enterprise to shadow Number One. While conducting communications experiments, Uhura broadcasts a recording of the song "Anything Goes" into a mysterious "subspace fold". It produces an "improbability field" that causes the Enterprise crew to begin singing about their feelings like characters in a musical film. Pike has an argument with Batel, in song, in front of the crew. Chapel wins a prestigious research fellowship and reveals in song that she prioritizes it over her relationship with Spock. La'An confesses her feelings for Kirk before the musical can force her to, but he is already in a relationship with Carol Marcus. An affected Klingon ship intends to blow up the fold, but experiments reveal this will destroy all starships in the fleet.

Summary from Wikipedia, CC BY-SA 4.0.